Theory stuff from sials work pc; minor stuff here and there

2026-02-19 15:11:32 +01:00
parent 1b8d83dec0
commit 2a724b833f
14 changed files with 810 additions and 39 deletions
--- a/Functions/Theory/Dissertation/photo_diode.m
+++ b/Functions/Theory/Dissertation/photo_diode.m
@@ -0,0 +1,124 @@
+%% ============================================================
+%  SNR vs Optical Input Power (dBm) — Shot vs Thermal vs Combined
+%  - Generate optical field as sine with target RMS power (verified)
+%  - Magnitude-square detection -> optical power
+%  - Photocurrent = Rd * P
+%  - Add shot noise + thermal noise (white, PSD-based)
+%  - Compute SNR for: shot-only, thermal-only, combined
+% ============================================================
+
+
+% Constants
+k = Constant.Boltzmann;
+q = Constant.ElementaryCharge;
+
+% Receiver / PD parameters
+T  = 20 + 273.15;      % K
+R  = 50;               % Ohm (front-end/load)
+Rd = 0.7;              % A/W (responsivity)
+Be = 100e9;            % Hz  (electrical noise bandwidth)
+Id = 0;                % A   (dark current, optional)
+
+% Sampling for time-domain demo (needs to be >> Be)
+fs   = 1e12;           % Hz
+N    = 2^14;           % samples
+t    = (0:N-1).'/fs;
+
+% Choose an electrical tone within bandwidth (arbitrary for demo)
+f0 = 10e9;             % Hz
+
+% Thermal current PSD (two-sided) and variance in Be
+Si_th    = 4*k*T/R;            % A^2/Hz (two-sided)
+sigma2_th = Si_th * Be;        % A^2
+sigma_th  = sqrt(sigma2_th);   % A_rms
+
+% Optical input power sweep (in dBm)
+P_dBm = linspace(-40, 10, 300);
+P_W   = 10.^((P_dBm - 30)/10); % W
+
+% Pre-allocate results
+SNR_shot_dB = zeros(size(P_dBm));
+SNR_th_dB   = zeros(size(P_dBm));
+SNR_tot_dB  = zeros(size(P_dBm));
+
+% --- Main loop over optical input power
+for ii = 1:numel(P_W)
+    Pavg = P_W(ii);
+
+    % Optical field with RMS power = Pavg:
+    % Let x(t) be the optical field amplitude such that |x|^2 has mean Pavg.
+    % Use a sinusoid: x(t) = A*sin(2*pi*f0*t), then mean(|x|^2)=A^2/2.
+    A = sqrt(2*Pavg);                      % -> mean(|x|^2) = Pavg
+
+    x = A * sin(2*pi*f0*t);                % "optical field" (real for simplicity)
+
+    % Verify RMS/mean power numerically (optional)
+    P_meas = mean(abs(x).^2);              % should be ~ Pavg
+
+    a = P_meas - Pavg;
+    assert(a<1);
+
+    % Magnitude-square detection -> optical power waveform
+    Popt = abs(x).^2;                      % W (instantaneous)
+
+    % Photocurrent waveform (includes DC + 2f0 component for this demo)
+    I_sig = Rd * Popt;                     % A
+
+    % Define "signal power" as the mean-squared photocurrent due to signal
+    % (for this sine-squared waveform, it's OK for a demo SNR definition)
+    P_sig = mean(I_sig.^2);
+
+    % -------- Shot noise (white) --------
+    % Two-sided PSD: Si_shot = 2*q*(I_photo + I_dark)
+    % For this demo, use average current to set the white-noise level:
+    Ibar = mean(I_sig) + Id;
+    Si_shot   = 2*q*Ibar;                  % A^2/Hz
+    sigma2_sh = Si_shot * Be;              % A^2
+    sigma_sh  = sqrt(sigma2_sh);           % A_rms
+
+    n_sh = sigma_sh * randn(N,1);          % time-domain shot noise
+
+    % -------- Thermal noise (white Gaussian) --------
+    n_th = sigma_th * randn(N,1);          % time-domain thermal noise
+
+    % Noise powers (mean-square) in time domain
+    Pn_sh = mean(n_sh.^2);
+    Pn_th = mean(n_th.^2);
+    Pn_tot = mean((n_sh + n_th).^2);       % ~ Pn_sh + Pn_th (independent)
+
+    % SNRs
+    SNR_shot = P_sig / Pn_sh;
+    SNR_th   = P_sig / Pn_th;
+    SNR_tot  = P_sig / Pn_tot;
+
+    SNR_shot_dB(ii) = 10*log10(SNR_shot);
+    SNR_th_dB(ii)   = 10*log10(SNR_th);
+    SNR_tot_dB(ii)  = 10*log10(SNR_tot);
+
+    % Optional sanity check (can comment out)
+    % if ii == 1
+    %     fprintf('Check Pavg target/meas: %.3g W / %.3g W\n', Pavg, P_meas);
+    % end
+end
+
+% Plot comparison
+figure(1); clf; hold on;
+plot(P_dBm, SNR_shot_dB, 'LineWidth', 1.5);
+plot(P_dBm, SNR_th_dB,   'LineWidth', 1.5);
+plot(P_dBm, SNR_tot_dB,  'LineWidth', 1.5);
+grid on;
+xlabel('Optical input power [dBm]');
+ylabel('SNR [dB]');
+title('SNR vs Optical Input Power: Shot vs Thermal vs Combined');
+legend('Shot-noise only','Thermal-noise only','Shot + Thermal','Location','best');
+
+% Print example at 0 dBm
+[~,idx0] = min(abs(P_dBm - 0));
+fprintf('At 0 dBm:\n');
+fprintf('  SNR (shot only)    = %.2f dB\n', SNR_shot_dB(idx0));
+fprintf('  SNR (thermal only) = %.2f dB\n', SNR_th_dB(idx0));
+fprintf('  SNR (combined)     = %.2f dB\n', SNR_tot_dB(idx0));
+
+% Also print NEP based on thermal PSD (constant NEP_th)
+NEP_th = sqrt(Si_th)/Rd; % W/sqrt(Hz)
+fprintf('Thermal NEP = %.3g W/sqrt(Hz)\n', NEP_th);